Substitute

, so that

![\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dz}+\dfrac1x\left(\dfrac1x\dfrac{\mathrm d^2y}{\mathrm dz^2}\right)=\dfrac1{x^2}\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dx%5E2%7D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1x%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dz%7D%5Cright%5D%3D-%5Cdfrac1%7Bx%5E2%7D%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dz%7D%2B%5Cdfrac1x%5Cleft%28%5Cdfrac1x%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dz%5E2%7D%5Cright%29%3D%5Cdfrac1%7Bx%5E2%7D%5Cleft%28%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dz%5E2%7D-%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dz%7D%5Cright%29)
Then the ODE becomes


which has the characteristic equation

with roots at

. This means the characteristic solution for

is

and in terms of

, this is

From the given initial conditions, we find


so the particular solution to the IVP is
Answer:
0.71 to 2 decimal places.
Step-by-step explanation:
The Probability that a letter A through G is drawn in 1 draw = 7/26.
The probability that a different draw other A-G is made = 1 - 7/26 = 19/26.
Probability ( No A-G drawn in 4 draws) = (19/26)^4 = 0.2852.
Therefore, the probability that A-G is drawn at least once = 1 - 0.2852.
= 0.71 to 2 decimal places.
9514 1404 393
Answer:
Step-by-step explanation:
Your knowledge of multiplication facts tells you 3×5 = 15. Your knowledge of addition facts tells you 3+2 = 5. So, the dimensions 3 cm and 5 cm are the width and length of the rectangle, respectively.
Perfect Square Trinomials have first and last terms that are positive perfect squares. And the middle term is
twice the product of the square roots of the first and third terms.
First term:
n^2
Square root = n

Third term:
9
Square root = 3

9 * 1 = 9
9 * 2 = 18
18

-9
Therefore it is not a perfect square trinomial.